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Finding the Linearization of a Function To find the linearization of a function f(x) at a specific point a, we use the formula: L(x) = f(a) + f'(a)(x – a) Step-by-step Process: Identify the function: In this case, we have f(x) = 9. This is a constant function. Determine the point of linearization: We want … Read more

To find the remainder when the polynomial 5x² + 10x + 15 is divided by x – 5, we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial f(x) by x – c is equal to f(c). In this case, our polynomial f(x) is 5x² + … Read more

To determine the number of real and imaginary zeros of the function f(x) = x³ + 5x² + x + 5, we can use methods such as the Rational Root Theorem, Synthetic Division, and the Descartes’ Rule of Signs. 1. **Familiarize with the function:** The given polynomial is a cubic function, which means it can … Read more

Solving the Equation x² + 4x + 12 = 0 The equation you provided is a quadratic equation in the standard form Ax² + Bx + C = 0, where A = 1, B = 4, and C = 12. To solve this equation, we can use the quadratic formula: x = (-B ± √(B² … Read more

To find the probability of getting exactly 6 heads when flipping a fair coin 9 times, we can use the binomial probability formula. The binomial probability formula is: P(X = k) = C(n, k) * p^k * (1-p)^(n-k) Where: P(X = k) is the probability of getting exactly k successes in n trials. C(n, k) … Read more

To calculate the average speed of the cyclist over the three hours, we first need to determine the total distance traveled and the total time taken. Total Distance: Distance in the first hour: 1 km Distance in the second hour: 5 km Distance in the third hour: 3 km Total distance = 1 km + … Read more

Classifying mathematical expressions involves understanding two key concepts: the number of terms in each expression and the degree of those terms. 1. Classification by Number of Terms: An expression can be classified into three categories based on its number of terms: Monomial: An expression with a single term. Example: 5x

To find the slope of the tangent line to a polar curve given by the equation r(θ) = 2 sin(θ) at the specific point where θ = π/3, we follow these steps: 1. Calculate r at θ = π/3 Substituting θ = π/3 into the equation, we get: r(π/3) = 2 sin(π/3) = 2 * … Read more

The theoretical probability of an event is a measure of the likelihood that event will occur, calculated based on the possible outcomes. In the case of tossing a fair coin, there are two possible outcomes for each toss: heads (H) and tails (T). When tossing a coin twice, we can list out all the possible … Read more